LCM of 6, 8 and 15 is 120. LCM is the short form for Least Common Multiple or the Lowest common multiple. LCM is also known as LCD which stands for Least Common Divisor. A common multiple for two or more numbers which is also the smallest number is called the LCM. Alternately, LCM and LCD are interconvertible. The smallest common multiple for all these numbers among many is 120, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 6, 8 and 15
The Least Common Multiple or Lowest Common Multiple of 6, 8 and 15 is 120.
How to Find LCM of 6, 8 and 15?
LCM of 6, 8 and 15 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 8 and 15 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 8 and 15 are expressed as;
6 = 2 × 3
8 = 2 × 2 × 2
15 = 3 × 5
Product of the union of the prime factors, forms the LCM.
Therefore, LCM(6, 8 and 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 6, 8 and 15 Using Division Method
In the Division Method, following steps are performed
- We divide the numbers 6, 8 and 15 starting with the smallest prime number which is 2. Only 6 and 8 are divisible.
- The division is continued in increasing order of prime divisors.
- The division is considered complete once the remainders become 1.
- The product of the prime divisors forms the LCM.
|
2 |
6 |
8 |
15 |
|
2 |
3 |
4 |
15 |
|
2 |
3 |
2 |
15 |
|
3 |
3 |
1 |
15 |
|
5 |
1 |
1 |
5 |
|
× |
1 |
1 |
1 |
LCM(6, 8 and 15) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 6, 8 and 15 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 6, 8 and 15
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132
Multiples of 8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136
Multiples of 15
15, 30, 45, 60, 75, 90, 105, 120, 135, 150
LCM(6, 8 and 15) = 120
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 8 and 15?
Answer: 120 is the smallest number that is divisible by 6, 8 and 15.
What is the LCM of 12 and 120?
Answer: LCM of 12 and 120 is 120 as 120 is the multiple of 12.
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